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Area of compound shapes Quiz

Grade 3 • 3X • 10 Questions (33 Marks)

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Score: 0 / 10
Area of compound shapes — Notes & Worked Examples Show / Hide

Explanation:

A compound (composite) shape is made up of two or more simple shapes joined together. To find its area, draw a dotted line to split it into rectangles or triangles, work out any missing side lengths first by comparing parallel horizontal and vertical sides, and then add the separate areas together.

Remember the key area formulas: Rectangle = length × width, and Triangle = 12 × base × perpendicular height. For shaded region questions, calculate the outer area minus the unshaded inner area.

Example 1: An L-shape has total width 10 cm, total height 8 cm, top width 4 cm, and right height 3 cm. Find its area.

4 cm 8 cm 10 cm 3 6 cm
Left = 4 × 8 = 32 cm²
Right = (10−4) × 3 = 18 cm²
Total = 32 + 18 = 50 cm²

Example 2: A pentagon has a 6 m by 4 m rectangular base and a triangle on top. Total height is 7 m. Find the area.

6 m 4 m 3 m 7 m
Rect = 6 × 4 = 24 m²
Tri h = 7 − 4 = 3 m
Tri = 12×6×3 = 9 m² → 33 m²
Question 1
[2 marks]
4 cm9 cm8 cm4 cm
Find the area of the compound shape
cm²
Worked Solution & Answer
(4 × 9) + (4 × 4) = 52 cm2 B1
Answer: 52 cm2 cm²
Question 2
[2 marks]
5cm9cm7cm8cm
Calculate the total area of the shape
cm²
Worked Solution & Answer
Area of a rectangle = length × width
51 cm2
Answer: 51 cm2 cm²
Question 3 Specimen Set 1 1F Q16
[2 marks]
2 cm10 cm8 cm2 cm
Work out the area of the L-shape.
Work out the area of the shape.
cm²
Worked Solution & Answer
(10 × 2) + (6 × 2) = 20 + 12 = 32 cm² (or (8 × 2) + (8 × 2) = 32 cm²) M1 A1
Answer: 32 cm²
Question Paper (PDF) • Mark Scheme (PDF)
Question 4 IGCSE Jun 2022 2F Q10
[3 marks]
The diagram shows a kite drawn on a centimetre grid.
On the centimetre grid below, draw a rectangle that has the same area as the kite.
Worked Solution & Answer
(The area of a rectangle is length × width)
Area of kite = ½ × 6 × 4 = 12 cm² M2
draw a 4 cm by 3 cm rectangle A1
On the centimetre grid below, draw a rectangle that has the same area as the kite.4 cm × 3 cm (12 cm²)
Answer: Any rectangle of area 12 cm² drawn on the grid (e.g. 4 cm × 3 cm, 6 cm × 2 cm, or 12 cm × 1 cm)
Question Paper (PDF) • Mark Scheme (PDF)
Question 5 AQA Jun 2023 1F Q15
[3 marks]
A large rectangle has a rectangular hole cut out.
Not drawnaccurately4 cm5 cm2 cm3 cm
Work out the percentage of the large rectangle that is shaded.
Answer %
Worked Solution & Answer
Area of large rectangle = 4 × 5 = 20 cm2 M1
Area of cut-out hole = 2 × 3 = 6 cm2 M1
Shaded area = 20 - 6 = 14 cm2
Percentage shaded = 1420 × 100% = 70%. A1
Answer: Answer 70 %
Question Paper (PDF) • Mark Scheme (PDF)
Question 6 IGCSE Jun 2021 1F Q18 / 1H Q3
[4 marks]
The diagram shows the shape ABCDE.
The area of the shape is 91.8 cm2
ABCDEx cm8 cm14 cm13 cmDiagram NOTaccurately drawn
Work out the value of x.
x =
Worked Solution & Answer
14x + ½ × 6 × (13 − x) = 11x + 39 = 91.8 M2
⇒ 11x = 52.8 M1
⇒ x = 4.8 A1
Answer: x = 4.8
Question Paper (PDF) • Mark Scheme (PDF)
Question 7 Specimen Set 1 1F Q23 / 1H Q4
[4 marks]
A pattern is made using identical rectangular tiles.
11 cm7 cm
Find the total area of the pattern.
cm²
Worked Solution & Answer
Let length = l and width = w. l + w = 7 and 2l + w = 11 ⇒ l = 4 cm, w = 3 cm M2
Area of 1 tile = 4 × 3 = 12 cm² M1
Total area = 4 × 12 = 48 cm². A1
Answer: 48 cm²
Question Paper (PDF) • Mark Scheme (PDF)
Question 8 IGCSE Jun 2025 1F Q17
[4 marks]
The diagram shows the plan of a stage.
The stage is made up of a rectangle and an isosceles triangle.
6 m8 m3 mDiagram NOTaccurately drawn
Yuko is going to cover the stage with varnish.
She needs to buy enough tins of varnish to cover the stage with one coat of varnish.
Each tin of varnish covers an area of 4 m2
Work out the smallest number of tins of varnish that Yuko needs to buy.
Show your working clearly.
Worked Solution & Answer
Rectangle area = 6 × 8 = 48 m² M1
Triangle area = ½ × 6 × 3 = 9 m² M1
Total area = 48 + 9 = 57 m² M1
57 ÷ 4 = 14.25 ⇒ 15 tins A1
Answer: 15
Question Paper (PDF) • Mark Scheme (PDF)
Question 9 AQA Nov 2020 2F Q16
[4 marks]
(a) Here is a shape made from rectangles.
Work out the area.
16 (b) Zak wants to work out the area of this triangle.
Here is his working.
12 × 8 = 96 cm2
What is wrong with his method?
(a) Here is a shape made from rectangles. [3 marks]
Not drawnaccurately9 cm8 cm4 cm2 cm
Work out the area.
Answer cm²
(b) Zak wants to work out the area of this triangle.
Here is his working.
12 × 8 = 96 cm2
What is wrong with his method? [1 mark]
Not drawnaccurately14 cm8 cm12 cm
Answer
Worked Solution & Answer
(a)
Split into two rectangles horizontally: M1
Top rectangle: 9 × 2 = 18 cm2 M1
Bottom rectangle: 4 × (8 - 2) = 4 × 6 = 24 cm2
Total area = 18 + 24 = 42 cm2 A1
Not drawnaccurately9 cm8 cm4 cm2 cm(9 × 2) + (4 × 6) = 42 cm²
Answer (a): Answer 42 cm²
(b)
(The area of a triangle is ½ × base × height)
The formula for the area of a triangle is 12 × base × perpendicular height , so he needed to divide by 2. B1
Answer (b): Answer He did not divide by 2 / area of triangle is 1/2 base x height
Question Paper (PDF) • Mark Scheme (PDF)
Question 10
[5 marks]
The diagram shows a plan of a floor.
Petra is going to cover the floor with paint.
Petra has 3 tins of paint.
There are 2.5 litres of paint in each tin.
Petra thinks 1 litre of paint will cover 10 m2 of floor.
10 m8 m6 m5 m
(a) Assuming Petra is correct, does she have enough paint to cover the floor?
You must show all your working. [4 marks]
(b) Does this affect your answer to part (a)?
You must give a reason for your answer. [1 mark]
Worked Solution & Answer
(a)
Area = 10 × 5 + 6 × 3 = 50 + 18 = 68 m² M3
Paint = 3 × 2.5 × 10 = 75 m² > 68 m², so Yes A1
Answer (a): Yes (Floor area = 68 m² and 3 tins cover 75 m²)
(b)
No effect, because the paint covers even more area (82.5 m²) so she will still have enough paint
Answer (b): No effect, because the paint covers even more area (82.5 m²) so she will still have enough paint
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 33 marks)
Area of compound shapes Worksheets Next: Frequency trees →

Grade 3 Quizzes

24 Topics
3A - Error intervals3B - Operations with fractions
3C - Estimation3D - Writing and simplifying ratio
3E - Ratio3F - Proportion recipes
3G - Percentages3H - Percentage change
3J - Exchange rates3K - Conversions and units
3L - Scale drawings3M - Best buy questions
3N - Substitution3P - Solving linear equations
3Q - Straight line graphs3R - Area and circumference
3S - Rotations3T - Reflections
3U - Enlargements3V - Translations
3W - Mixed transformations3X - Area of compound shapes
3Y - Frequency trees3Z - Two way tables